Question

The ratio of the equal sides to the base of an isosceles triangle is 3:1. If the perimeter
of the triangle is 28 cm, then find its area."
​

Answer 1

Answer:

4√35 cm²

Step-by-step explanation:

Let ABC be an isosceles triangle with perimeter 28 cm.

We have ratio of equal side to its base is 3:1.

Let sides of a triangle be AB = AC = 3x, BC = x

∴ Perimeter of triangle = 28 cm

⇒ 3x + 3x + x = 28

⇒ 7x = 28

⇒ x = 4 cm

∴ AB = AC = 3 * 4 = 12 cm

∴ BC = 4 cm

The sides of a triangle are,

a = 12 cm, b = 12 cm, c = 4 cm

S = (a + b + c)/2

  = (12 + 12 + 4)/2

 = 14 cm

∴ Area of an isosceles ΔABC,

= √s(s - a)(s - b)(s - c)

= √14(14 - 12)(14 - 12)(14 - 4)

= √14 * 2 * 2 * 10

= 4√35

Hence, area of an isosceles triangle = 4√35 cm²

Hope it helps!